In order to measure a three-dimensional shape, sensors based on various principles such as stereo, an light sectioning method, a focus, a blur, special encoding, and an optical radar have been proposed. However, since a sensor based on an optical principle uses an image sensor as a light-receiving element, in general, data is acquired as a range image in which three-dimensional shape information corresponds to pixels. The range image is an important input form of three-dimensional shape information for recognition of an object and shape model creation in the field of CV, CG, CAD, VR, and robots.
In many cases, in the range image, only a part of a surface of an object body can be measured. In order to create a shape model for an entire surface of an object, it is necessary to measure an object from various directions. Respective range images are represented by coordinate systems of the center of a sensor. To combine the range images into one shape model, it is necessary to calculate a positional relation among the respective range images. Estimation of such a positional relation from data is registration.
Registration of the range images can be divided into two stages, i.e., coarse registration and fine registration. At the stage of the coarse registration, registration for limiting errors among range images measured from completely different viewpoints within a certain degree of error range is performed. Once registration can be performed coarsely, it is possible to apply the fine registration with the coarse registration set as an initial value. An ICP (Iterative Closest Point) algorithm (see Non-Patent Document 1), a direct method (see Non-Patent Documents 2 and 3), and a modeling method by simultaneous registration (see Non-Patent Document 4) are registration methods belonging to a fine stage. The present invention proposed a registration method at a coarse stage and performs model creation by applying a fine registration method using the registration at the coarse stage as an initial value.
The coarse registration can be obtained by attaching a marker to an object, using an electromagnetic positioning device such as a GPS, or using an active device such as a turning table or a robot arm. However, depending on a size, a material, and a measurement environment of an object, such devices cannot always be used. Such information is not always provided together with data. It is also possible to manually apply the coarse registration using a GUI. However, when the number of data increases, since labor of work is large, it is desirable to support the work with a computer.
The coarse registration method is deeply related to researches performed as object recognition. A most representative method is a method of using a feature invariable with respect to a geometric transformation (in the case of a rigid body, a Euclidean transformation) for registration. A curvature is an invariable amount defined by differential geometry and can be mathematically calculated from an ultimately micro-area. In calculating a curvature from an actual range image, various contrivances have been proposed to stably calculate the curvature using data in a finite range (see Non-Patent Document 5). However, most of the contrivances are based on local application of some consecutive function to discrete data. In Feldmar and Ayache (see Non-Patent Document 6), coarse registration is performed by applying a RANSAC (a robust model estimation algorithm realized by repeatedly verifying, with all data, a hypothesis created on the basis of a minimum number of samples selected at random; see Non-Patent Document 30) to a set of local orthogonal bases formed by a main direction and the normal obtained in calculating a curvature. The curvature is represented by two components (maximum−minimum, Gaussian−average, or curvedness−shape index) (see Non-Patent Document 7) and is not always sufficient information for performing association. It is necessary to select the curvature from many candidates by methods such as random sampling and voting. It is possible to reduce searches for candidates and perform stable registration by also using more general information incidental to the curvature. In Kehtarnavaz and Mohan (see Non-Patent Document 8), areas divided according to a sign of a curvature are represented by a graph and registration is performed by partial graph matching. In Higuchi et al. (see Non-Patent Document 9), estimation of a rotation component is estimated by matching of amounts similar to a curvature mapped on a unit spherical surface. In Krsek et al. (see Non-Patent Document 10), matching of curved lines with an average curvature of 0 is performed by random sampling.
It can be said that a method of dividing an input shape into segments of partial shapes and matching segments represented by similar parameters uses a relatively significant characteristic. Faugeras and Herber divide a curved surface with a plane or a secondary curved surface and perform registration by verifying a hypothesis of a correspondence relation among divided segments (see Non-Patent Document 11). Kawai et al. (see Non-Patent Document 12), a triangular patch is used. In these methods based on segments, it is assumed that division into segments (segmentation) can be stably performed. However, corresponding segments are not always divided in the same manner in a free curved surface including noise or occlusion. In Wyngaerd and Van Gool (see Non-Patent Document 13), registration is performed using a bitangent curve drawn by a straight line that is in contact with a curved surface in two places.
A characteristic based on a micro-area has problems in stability and a description ability and a global characteristic has problems in stability of segmentation and robustness against occlusion. Stein and Medioni propose a feature called “splash” calculated from the normal of a curved surface on a circumference surrounding a center vertex (see Non-Patent Document 14). Chua and Jarvis propose a point signature calculated from a curved line obtained by projecting an intersection of a curved surface and a spherical surface on a tangential plane (see Non-Patent Document 15). Johnson and Hebert set, as a spin image, a histogram image of measurement points collected by rotating an image plane perpendicular to a tangential plane at a center vertex around the normal (see Non-Patent Document 16) and apply the spin image to symmetry recognition. In the spin image, corresponding point search is performed in a space dimensionally compressed by peculiar image expansion. Huber and Herbert propose a method of performing automatic registration of plural range images by using a spin image and combining the spin image with verification based on appearance (see Non-Patent Document 17). These methods are attempts to facilitate correspondence search by obtaining description of abundant information from an area wider than a curvature.
There is also an approach of solving registration by optimizing an error function describing a state of registration instead of performing association by features. A satisfactory initial value is not provided for coarse registration and a space of parameters to be searched is large. Thus, a probabilistic optimization method is used. Blais and Levine use simulated annealing (SA) (see Non-Patent Document 18) and Brunnstrom and Stoddart search for an optimum correspondence with a genetic algorithm (GA) (see Non-Patent Document 19). Sliva et al. solve registration of plural range images by optimizing registration parameters with a GA such that an error function is minimized (see Non-Patent Document 20). Such methods based on probabilistic optimization have to evaluate the error function an extremely large number of times.    Non-Patent Document 1: P. J. Besl and N. D. 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